# Journal of Mathematics and Statistics

## 3-Unit System Comprising Two Types of Units with First Come First Served Repair Pattern Except When Both Types of Units are Waiting for Repair

Amit Goyal, Gulshan Taneja and D. V. Singh

DOI : 10.3844/jmssp.2010.316.320

Journal of Mathematics and Statistics

Volume 6, Issue 3

Pages 316-320

### Abstract

Problem statement: In this study we investigated the probabilistic analysis of a three unit system working in a sugar Mill, wherein one unit is big and the other two units are small and identical, is examined. Upon failure of the big unit, both small units are made operative and failed unit is undertaken for repair immediately. Priority for operation is given to the big unit. Priority for repair is given to big unit if both types (i.e., big and small) of units are in queue to get the repair done. System is able to work with full capacity only if big unit or both small units are in good condition. If only one small unit is operable, the system works at reduced capacity. The system under consideration goes to rest during the non-seasonal period. Approach: System was analyzed by making use of semi-Markov processes and regenerative point technique and various measures of the system effectiveness are obtained including the profit incurred to the system. Results: Graphs had been plotted to depict the behavior of the profit with respect to failure rate for different values of repair rate and with respect to revenue per unit up time for which system is working at full capacity for different values of cost for PM/CM. Conclusion: The profit increases with the decrease in the values of the failure rate and with the increase in the values of revenue per unit up time. It has lower (higher) values on increasing the values of cost (repair rate). Cut-off points obtained for failure rate help decide about having the system with failure rate lesser than that the value at cut-off point. Also, the price of the product should be fixed in such a way so as to get the revenue greater than the value at cut-off point.